Editing Number line (section)

==Comparing numbers==
If a particular number is farther to the right on the number line than is another number, then the first number is greater than the second (equivalently, the second is less than the first). The distance between them is the magnitude of their difference&mdash;that is, it measures the first number minus the second one, or equivalently the absolute value of the second number minus the first one. Taking this difference is the process of [[subtraction]].

Thus, for example, the length of a [[line segment]] between 0 and some other number represents the magnitude of the latter number.

Two numbers can be [[added]] by "picking up" the length from 0 to one of the numbers, and putting it down again with the end that was 0 placed on top of the other number.

Two numbers can be [[multiplied]] as in this example: To multiply 5 × 3, note that this is the same as 5 + 5 + 5, so pick up the length from 0 to 5 and place it to the right of 5, and then pick up that length again and place it to the right of the previous result. This gives a result that is 3 combined lengths of 5 each; since the process ends at 15, we find that 5 × 3 = 15.

[[Division (mathematics)|Division]] can be performed as in the following example: To divide 6 by 2&mdash;that is, to find out how many times 2 goes into 6&mdash;note that the length from 0 to 2 lies at the beginning of the length from 0 to 6; pick up the former length and put it down again to the right of its original position, with the end formerly at 0 now placed at 2, and then move the length to the right of its latest position again. This puts the right end of the length 2 at the right end of the length from 0 to 6. Since three lengths of 2 filled the length 6, 2 goes into 6 three times (that is, 6 ÷ 2 = 3).

<gallery widths=300>
File:Number line with x smaller than y.svg|The ordering on the number line: Greater elements are in direction of the arrow.
File:Number line with addition of -2 and 3.svg|The difference 3−2=3+(−2) on the real number line
File:Number line with addition of 1 and 2.svg|The addition 1+2 on the real number line
File:Absolute difference.svg|The absolute difference.
File:Number line multiplication 2 with 1,5.svg|The multiplication 2×1.5 on the real number line
File:Number line division 3 with 2.svg|The division 3÷2 on the real number line
</gallery>